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An Affine Approach to Peterson Comparison
The Peterson comparison formula proved by Woodward relates the three-pointed Gromov-Witten invariants for the quantum cohomology of partial flag...
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A Positive Formula for Type A Peterson Schubert Calculus
The Peterson variety is a special case of a nilpotent Hessenberg variety, a class of subvarieties of G / B that have appeared in the study of quantum...
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Restricted secant varieties of Grassmannians
Restricted secant varieties of Grassmannians are constructed from sums of points corresponding to k -planes with the restriction that their...
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Perverse Sheaves and the Cohomology of Regular Hessenberg Varieties
We use the Springer correspondence to give a partial characterization of the irreducible representations which appear in the Tymoczko dot action of...
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Geometric Vertex Decomposition, Gröbner Bases, and Frobenius Splittings for Regular Nilpotent Hessenberg Varieties
We initiate a study of the Gröbner geometry of local defining ideals of Hessenberg varieties by studying the special case of regular nilpotent...
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AN ADDITIVE BASIS FOR THE COHOMOLOGY RINGS OF REGULAR NILPOTENT HESSENBERG VARIETIES
In this paper we construct an additive basis for the cohomology ring of a regular nilpotent Hessenberg variety which is obtained by extending all...
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Hessenberg varieties of parabolic type
This paper studies the geometry and combinatorics of three interrelated varieties: Springer fibers, Steinberg varieties, and parabolic Hessenberg...
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From Hyperbolic Dehn Filling to Surgeries in Representation Varieties
Hyperbolic Dehn surgery and the bending procedure provide two ways which can be used to describe hyperbolic deformations of a complete hyperbolic...
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Degenerate Affine Flag Varieties and Quiver Grassmannians
We study finite dimensional approximations to degenerate versions of affine flag varieties using quiver Grassmannians for cyclic quivers. We prove...
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FUNDAMENTAL GROUPS OF SPLIT REAL KAC-MOODY GROUPS AND GENERALIZED REAL FLAG MANIFOLDS
We determine the fundamental groups of symmetrizable algebraically simply connected split real Kac-Moody groups endowed with the Kac-Peterson...
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A filtration on the cohomology rings of regular nilpotent Hessenberg varieties
Let n be a positive integer. The main result of this manuscript is a construction of a filtration on the cohomology ring of a regular nilpotent...
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A Survey of Recent Developments on Hessenberg Varieties
This article surveys recent developments on Hessenberg varieties, emphasizing some of the rich connections of their cohomology and combinatorics. In...
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The partial compactification of the universal centralizer
The universal centralizer of a semisimple algebraic group G is the family of centralizers of regular elements, parametrized by their conjugacy...
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Unstable splittings in Hodge filtered Brown–Peterson cohomology
We construct Hodge filtered function spaces associated to infinite loop spaces. For Brown–Peterson cohomology, we show that the corresponding Hodge...
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Hessenberg varieties, Slodowy slices, and integrable systems
This work is intended to contextualize and enhance certain well-studied relationships between Hessenberg varieties and the Toda lattice, thereby...
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Isotropic and numerical equivalence for Chow groups and Morava K-theories
In this paper we prove the conjecture claiming that, over a flexible field, isotropic Chow groups coincide with numerical Chow groups (with
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